Place the noodles in a large heatproof bowl, pour over boiling water to cover and leave to stand for 5 minutes or until just tender.
Meanwhile, place the Singapore noodle paste in a large saucepan, add the beans and carrot and stir together thoroughly until the vegetables are coated in the spice mix. Cook, stirring, over a medium heat for 1–2 minutes.
Stir the coconut milk and hot stock into the pan, then add the bean sprouts and bamboo shoots and simmer for 3 minutes. Stir in the coriander and the lime juice.
Drain the noodles, divide between 4 warmed large deep bowls and ladle over the soup.
Top with the spring onions and chilli, if using, and serve immediately with lime wedges.